#!/usr/bin/env python3
#
# Generate manufactured solution and sources for FCI test
#

from __future__ import division
from __future__ import print_function

from boutdata.mms import *

from sympy import sin, cos, sqrt

from math import pi

f = sin(y - z) + sin(y - 2*z)

Lx = 0.1
Ly = 10.
Lz = 1.

Bt = 1.0
Bp = 0.05
Bpprime = 0.1

Bpx = Bp + (x-0.5)*Lx * Bpprime  # Note: x in range [0,1]
B = sqrt(Bpx**2 + Bt**2)

def FCI_ddy(f):
    return ( Bt * diff(f, y)*2.*pi/Ly + Bpx * diff(f, z)*2.*pi/Lz ) / B

############################################
# Equations solved

print("input = " + exprToStr(f))
print("solution = " + exprToStr(FCI_ddy(f)))
